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방원도의 투영

Squaring the Circle in Perspective

  • 투고 : 2014.10.24
  • 심사 : 2014.12.18
  • 발행 : 2014.12.31

초록

When the circle inscribed in a square is projected to a picture plane, one sees, in general, an ellipse in a convex quadrilateral. This ellipse is poorly described in the works of Alberti and Durer. There are one parameter family of ellipses inscribed in a convex quadrilateral. Among them only one ellipse is the perspective image of the circle inscribed in the square. We call this ellipse "the projected ellipse." One can easily find the four tangential points of the projected ellipse and the quadrilateral. Then we show how to find the center of the projected ellipse. Finally, we describe a pair of conjugate vectors for the projected ellipse, which finishes the construction of the desired ellipse. Using this algorithm, one can draw the perspective image of the squared-circle tiling.

키워드

참고문헌

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  8. E. Panofsky, The Life and Art of Albrecht Durer, Princeton Univ. Press, 1943. (에르빈 파 노프스키 지음, 이산 옮김, 인문주의 예술가 뒤러, 한길아트, 2006.)